## Calculus: Early Transcendentals (2nd Edition)

A number $M = f(c)$ is a local maximum for $f$ if there is an interval $(r, s)$ containing $c$ so that $f(x) ≤ M$ for all $x \in (r, s)$. A number $m = f(d)$ is a local minimum for $f$ if there is an interval $(r, s)$ containing $d$ so that $f(x) ≥ m$ for all $x \in (r, s)$.